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Zap. Nauchn. Sem. POMI, 1995, Volume 221, Pages 145–166 (Mi znsl4301)  
The Bergman kernel and the Green function

V. A. Malyshev

Rybinsk State Aviation Technological Academy

Abstract: Definition of the Bergman space for an arbitrary operator is given. Sufficient conditions for the existence of the Bergman kernel for this space are obtained. For an elliptic operator, the Bergman kernel is represented via the Green function. Bibliography: 12 titles.

Full text: PDF file (662 kB)

English version:
Journal of Mathematical Sciences (New York), 1997, 87:2, 3366–3380

Bibliographic databases:

UDC: 519.632
Received: 10.01.1995

Citation: V. A. Malyshev, “The Bergman kernel and the Green function”, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Zap. Nauchn. Sem. POMI, 221, POMI, St. Petersburg, 1995, 145–166; J. Math. Sci. (New York), 87:2 (1997), 3366–3380

Citation in format AMSBIB
\Bibitem{Mal95}
\by V.~A.~Malyshev
\paper The Bergman kernel and the Green function
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 221
\pages 145--166
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1359754}
\zmath{https://zbmath.org/?q=an:0927.32001|0885.32021}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 2
\pages 3366--3380
\crossref{https://doi.org/10.1007/BF02355588}


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